Approximate sparsity patterns for the inverse of a matrix and preconditioning

Thomas Huckle

doi:10.1016/S0168-9274(98)00117-2

Approximate sparsity patterns for the inverse of a matrix and preconditioning

Thomas Huckle

Informatics 5 - Chair of Scientific Computing

Research output: Contribution to journal › Conference article › peer-review

100 Scopus citations

Abstract

This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A^-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A^-1 are developed using the characteristic polynomials and the Neumann series associated with A and A^T A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.

Original language	English
Pages (from-to)	291-303
Number of pages	13
Journal	Applied Numerical Mathematics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/S0168-9274(98)00117-2
State	Published - Jun 1999
Event	Proceedings of the 1997 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics - Berlin, Ger Duration: 24 Aug 1997 → 29 Aug 1997

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10.1016/S0168-9274(98)00117-2

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abstract = "This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A-1 are developed using the characteristic polynomials and the Neumann series associated with A and AT A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.",

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AB - This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A-1 are developed using the characteristic polynomials and the Neumann series associated with A and AT A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.

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DO - 10.1016/S0168-9274(98)00117-2

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T2 - Proceedings of the 1997 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics

Y2 - 24 August 1997 through 29 August 1997

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Approximate sparsity patterns for the inverse of a matrix and preconditioning

Abstract

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